Three tugboats are used to bring a large ship to a pier as shown. Each tugboat exerts a 4000 lb force pushing toward the large ship. Determine an equivalent force and couple system at point A.
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Three tugboats are used to bring a large ship to a pier as shown. Each tugboat exerts a 4000 lb force pushing toward the large ship. Determine an equivalent force and couple system at point A.
Explanation:
The net vertical force will be;
Fy = 4000lb*(sin45º - 4/5 - 1) = -4372 lb (i.e, down)
net horizontal force
Fx = 4000lb*(cos45º + 3/5) = 5228 lb
equivalent force F = √(Fx² + Fy²) = 6815 lb
net torque about A, taking ccw as positive
τ = 4000lb*(50*cos45º + 250*sin45º - 400 - 100*4/5 - 50*3/5)ft
τ = -1.1915E6 lb·ft
The figure is attached below
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